You will investigate this task using Graph2 or similar graphing software. Your finished project should be word processed, and ideally presented in a blog that will help you to put together a maths portfolio of work. You should make sure you are communicating your work clearly and explaining WHY things work the way they do.
Plot the graph of y = f(x) where f(x) = x^2. Find the gradient at various points along the graph, and record your findings in a table, something like this:
f(x)
-5
-4
-3
-2
-1
0
1
2
3
gradient f'(x)
-10
0
Can you suggest what the gradient function is?
Try the same thing for y = f(x) + 3, y = f(x) - 2. Can you make a general statement about y = f(x) + c? Why does it work like this?
What about y = 2f(x)? y = 0.5 f(x)? Can you make a general statement for a f(x)? Why does it work like this?
What happens for f(x) = x^3? f(x) =x^4?
If you have found a general rule and described it adequately, try to find gradient functions for some or all of the following:
Gradients of Lines and Curves
You will investigate this task using Graph2 or similar graphing software. Your finished project should be word processed, and ideally presented in a blog that will help you to put together a maths portfolio of work. You should make sure you are communicating your work clearly and explaining WHY things work the way they do.
Plot the graph of y = f(x) where f(x) = x^2. Find the gradient at various points along the graph, and record your findings in a table, something like this:
Can you suggest what the gradient function is?
Try the same thing for y = f(x) + 3, y = f(x) - 2. Can you make a general statement about y = f(x) + c? Why does it work like this?
What about y = 2f(x)? y = 0.5 f(x)? Can you make a general statement for a f(x)? Why does it work like this?
What happens for f(x) = x^3? f(x) =x^4?
If you have found a general rule and described it adequately, try to find gradient functions for some or all of the following:
f(x) = sin x
f(x) = cos x
f(x) = e^x